EIT Review Electrical Circuits DC Circuits Lecturer: Russ Tatro Presented by Tau Beta Pi The Engineering Honor Society 10/3/2006 1
Session Outline Basic Concepts Basic Laws Methods of Analysis Circuit Theorems Operational Amplifiers Capacitors and Inductors Summary and Questions 10/3/2006 2
Basic Concepts Linear, Lumped parameter systems. Linear response is proportional to V or I (no higher order terms needed) Lumped Parameter Electrical effects happen instantaneously in the system. Low frequency or small size (about 1/10 of the wavelength). 10/3/2006 3
Basic Concepts 10/3/2006 4
Basic Concepts - Units Volt The Potential difference is the energy required to move a unit charge (the electron) through an element (such as a resistor). Amp Electric current is the time rate of change of the charge, measured in amperes (A). A direct Current (dc) is a current that remains constant with time. An alternating current (ac) is a current that varies sinusoidally with time. Ohm the resistance R of an element denotes its ability to resist the flow of electric current; it is measured in ohms (Ω). 10/3/2006 5
Basic Concepts - Units Farad Capacitance is the ratio of the charge on one plate of a capacitor to the voltage difference between the two plates, measured in farads (F). Henry Inductance is the property whereby an inductor exhibits opposition to the charge of current flowing through it; measured in henrys (H). 10/3/2006 6
Basic Concepts - Volts Symbol: V or E (electromotive force) Circuit usage: V or v(t) when voltage may vary. Voltage is a measure of the DIFFERENCE in electrical potential between two points. I say again! Voltage ACROSS two points. 10/3/2006 7
Basic Concepts - Amps Symbol: A (Coulomb per second) Circuit usage: I or i(t) when current may vary with time. Amperage is a measure of the current flow past a point. I say again! Current THRU a circuit element. 10/3/2006 8
Basic Concepts - Ohms Symbol: Ω Circuit usage: R Resistance is the capacity of a component to oppose the flow of electrical current. R = V/I 10/3/2006 9
Basic Concepts - Farad Symbol: F Circuit usage: C for capacitor Capacitor resists CHANGE in voltage across it. Passive charge storage by separation of charge. Electric field energy. 10/3/2006 10
Basic Concepts - Henrys Symbol: H Circuit usage: L for inductor Inductor resists CHANGE in current thru it. Passive energy storage by creation of magnetic field. 10/3/2006 11
Basic Concepts Passive Sign Convention Use a positive sign when: Current is the direction of voltage drop. 10/3/2006 12
Basic Concepts Power p = (+/-) vi = i 2 R = v 2 /R p = the power in watts v = the voltage in volts I = the current in amperes I.A.W. with Passive Sign Convention + (positive) element is absorbing power. - (negative) element is delivering power. 10/3/2006 13
Basic Concepts - Example Power delivered/absorbed. 10/3/2006 14
Basic Concepts End of Basic Concepts. Questions? 10/3/2006 15
Basic Laws Circuit Connections: Nodes point of connection of two or more branches. Branches single element. Loops any CLOSED path in a circuit. 10/3/2006 16
Basic Laws Ohm s Law Ohms Law: v = ir R = v/i 1 Ω = 1 V/A Short Circuit when R = 0 Ω Open Circuit when R = Ω 10/3/2006 17
Basic Laws - Kirchhoff s Laws KVL: Kirchhoff s Voltage Law Sum of all voltages around a closed path is zero. KCL: Kirchhoff s Current Law Sum of all currents = zero sum all currents in = sum all currents out Based on conservation of charge: 10/3/2006 18
Basic Laws Series/Parallel Series Resistors: Req = R1 + R2 + Parallel Resistors: 1 R eq = 1 R 1 + 1 R 2 +... For Two Resistors in Parallel: = R R2 R R 1 eq R + 1 2 10/3/2006 19
Basic Laws Voltage Divider Voltage Divider for Series Resistors: v 1 = R 1 R + 1 R 2 v v 2 = R 1 R + 2 R 2 v 10/3/2006 20
Basic Laws Current Divider Current Divider for Parallel Resistors: i 1 = R 1 R + 2 R 2 i i 2 = R 1 R + 1 R 2 i 10/3/2006 21
Basic Laws Example KCL/KVL Example 10/3/2006 22
Basic Laws Example Calculating Resistance R eq =? R eq =? 10/3/2006 23
Basic Laws Example Voltage Divider 10/3/2006 24
Basic Laws Example Current Divider 10/3/2006 25
Basic Laws Questions? 10/3/2006 26
Break for 5 minutes. Chinese Proverb: This too shall pass. Or as the Kidney stone patient hopes: This too shall pass, but not soon enough! 10/3/2006 27
Methods of Analysis Nodal Analysis assign voltages in branches and find currents. Mesh Analysis assign currents in a loop and find voltages. 10/3/2006 28
Methods of Analysis Node Analysis: 1. Select a reference node. 2. Apply KCL to each of the nonreference nodes. 3. Solve the resulting simultaneous equations. Number of equations = # of nodes - 1 10/3/2006 29
Methods of Analysis Node Analysis: Select a reference node. This becomes the zero reference. All voltages become a rise in voltage from this reference node. 10/3/2006 30
Methods of Analysis Node Analysis: Apply KCL: There are a number of slightly different approaches in applying KCL. The approach you use MUST be consistent! IMHO assume voltage drop away from node. This means the current is leaving the node. IMHO in my humble opinion 10/3/2006 31
Methods of Analysis Example Let us work a node problem. 10/3/2006 32
Methods of Analysis Supernode: when a voltage source connects to nonreference nodes. Recall that a ideal voltage source provides WHATEVER current the circuit requires. Procedure: 1. Short the voltage source. That is: form a single node of the ends of the voltage source. 2. Write the constraint equation for the voltages. 3. Write the standard node equations for the supernode. 10/3/2006 33
Methods of Analysis Remember the constraint equation! v 1 2V = v 2 10/3/2006 34
Methods of Analysis Mesh Analysis: A mesh is a loop which does not contain any other loops within it. 1. Assign mesh currents to the n meshes. 2. Apply KVL to each mesh. Express the voltages in terms of Ohm s law. 3. Solve the resulting n simultaneous equations. 10/3/2006 35
Methods of Analysis Example Let us work a mesh problem. 10/3/2006 36
Methods of Analysis Supermesh: when two meshes share a current source. Recall that a ideal current source provides WHATEVER voltage the circuit requires. Procedure: 1. Open the current source. That is form a single mesh for the two mesh sharing the current source. 2. Write the constraint equation for the currents. 3. Write the standard mesh equation for the supermesh. 10/3/2006 37
Methods of Analysis Remember to write the constraint equation! i 1 6A i 2 = 0 10/3/2006 38
Methods of Analysis Supermesh or Supernode? 1. Do what the test tells you! 2. Pick the approach with the least equations. 3. Node equations are usually easier. 10/3/2006 39
Methods of Analysis End of Methods of Analysis. Questions? 10/3/2006 40
Circuit Theorems 1. Superposition 2. Source Transformation 3. Thevenin s Theorem 4. Norton s Theorem 5. Maximum Power Transfer 10/3/2006 41
Circuit Theorems - Superposition Determine the contribution of each independent source to the variable in question. Then sum these responses to find the total response. 10/3/2006 42
Circuit Theorems - Superposition 1. Turn off all independent sources except one. Voltage source V = 0 when shorted. Current source A = 0 when opened. 2. Solve the circuit. 3. Repeat until all sources handled. 4. Sum the individual responses to get the total response. 10/3/2006 43
Circuit Theorems Source Transforms A source transformation exchanges a voltage source with a series resistor with a current source and a parallel resistor. v s = i s R i s = v s R 10/3/2006 44
Circuit Theorems Example Let us work a source transformation problem. 10/3/2006 45
Circuit Theorems Example Let us work a source transformation problem. 10/3/2006 46
Circuit Theorems Thevenin s Theorem Thevenin s Theorem: a linear two-terminal network can be replaced with an equivalent circuit of a single voltage source and a series resistor. V TH is the open circuit voltage R TH is the equivalent resistance of the circuit. 10/3/2006 47
Circuit Theorems Thevenin s Theorem 10/3/2006 48
Circuit Theorems Example Let us work a Thevenin problem. 10/3/2006 49
Circuit Theorems Example Let us work a Thevenin problem. 10/3/2006 50
Circuit Theorems Norton s Theorem Norton s Theorem: a linear two-terminal network can be replaced with an equivalent circuit of a single current source and a parallel resistor. I = N V R TH TH I N is the short circuit current. R TH is the equivalent resistance of the circuit. 10/3/2006 51
Circuit Theorems Example Let us work a Norton problem. 10/3/2006 52
Circuit Theorems Example 10/3/2006 53
Circuit Theorems Maximum Power Transfer The maximum power delivered to a load is when the load resistance equals the Thevenin resistance as seen from the load. R = R L TH 10/3/2006 54
Circuit Theorems Maximum Power Transfer When R = R L TH Then p max = V 4R 2 TH TH 10/3/2006 55
Circuit Theorems End of Circuit Theorems. Questions? 10/3/2006 56
Break for 5 minutes. Nerves and butterflies are fine - they're a physical sign that you're mentally ready and eager. You have to get the butterflies to fly in formation, that's the trick. ~Steve Bull 10/3/2006 57
Operational Amplifiers OP Amp name derived from this circuits ability to perform various mathematical operations. Why us? Another chance to use Node Analysis! When not? Op Amp with capacitor or inductor? No Laplace skills? Then guess an answer and move along. 10/3/2006 58
Operational Amplifiers Ideal Op Amp assumptions: 1. i n = i p = zero 2. v n = v p 3. V out is equal to or less than the input power voltage. V ± V out CC 10/3/2006 59
Operational Amplifiers Use node analysis to solve the problem. If you recognize the type and like to memorize: Inverting Op Amp: V out = R feedback R input V input Noninverting Op Amp: V out = 1+ R feedback R input V input 10/3/2006 60
Operational Amplifiers Example Let us work an Op Amp problem. 10/3/2006 61
Operational Amplifiers End of Operational Amplifiers. Questions? 10/3/2006 62
Capacitors and Inductors A Capacitor consists of two conducting plates separated by an insulator. Capacitance is the ratio of the charge on one plate of a capacitor to the voltage difference between the two plates. Capacitance is measured in Farads. 10/3/2006 63
Capacitors and Inductors The voltage across a capacitor cannot change abruptly. i = C dv dt A capacitor is an open circuit to dc. 10/3/2006 64
Capacitors and Inductors Capacitors add in parallel - CAP C eq = C C + + 1 2... Series Capacitance 1 C eq = 1 C 1 + 1 C 2 +... 10/3/2006 65
Capacitors and Inductors An Inductor consists of a coil of conducting wire. Inductance is the property where an inductor opposes change to current flow. Inductance is measured in Henrys. 10/3/2006 66
Capacitors and Inductors The current thru an inductor cannot change abruptly. v = L di dt An inductor is a short circuit to dc. 10/3/2006 67
Capacitors and Inductors Inductors add in series. L eq = L L + + 1 2... Parallel Inductance 1 L eq = 1 L 1 + 1 L 2 +... 10/3/2006 68
Capacitors and Inductors Example Overall behavior of an inductor 10/3/2006 69
Capacitors and Inductors Example Overall behavior of an inductor 10/3/2006 70
Capacitors and Inductors Example Overall behavior of a capacitor 10/3/2006 71
Capacitors and Inductors End of Capacitors and Inductors. Questions? 10/3/2006 72
Summary Passive Sign Power: p = vi Ohm s Law v = ir = i 2 R = V 2 /R KCL Sum of currents = zero KVL Sum of voltage in loop = zero Series/Parallel Elements Voltage/Current Divider 10/3/2006 73
Summary Source Transformation Thevenin Equivalent Norton Equivalent Ideal Op Amp Capacitor Inductor 10/3/2006 74
Summary What we did not cover: Response of 1 st order RC/RL circuits Unbounded response Response of 2 nd order RLC circuits Sinusoidal Steady-State analysis 3 Phase AC power Be sure to study these areas as time permits. 10/3/2006 75
Good Luck on the EIT Exam! It is a timed exam. Answer what you know. Mark what you might know and come back later. Do not get bogged down on a few questions. Move along! Remember that it is a multiple choice exam. Look for hints in the answers. If totally in doubt Guess by using your intuition and science. 10/3/2006 76
EIT Review Electrical Circuits DC Circuits Lecturer: Russ Tatro Presented by Tau Beta Pi The Engineering Honor Society 10/3/2006 77